Exact solutions of the Lotka-Volterra system with cross-diffusion
A system of two reaction-diffusion equations with cross-diffusion and quadratic nonlinearities are considered. The system contains as a particular case the well-known model proposed by Shigesada et all in 1979. New non-Lie Ansatze reducing the system to the ordinary differential equations system are obtained. Several families of exact solutions are constructed and their asymptotic behaviour are investigated. Some biological interpretation of the solutions are provided.
Joint work with Roman Cherniha.